<p>This paper proposes a novel three-directional functionally graded (3D FG) vibration energy harvesting model based on a bimorph pipe structure. A rectangular pipe has material properties that vary continuously along the axial, width, and height directions, and a steady fluid flows inside the pipe. Two piezoelectric layers are attached to the upper and lower surfaces of the pipe, and are connected in series with a load resistance. The output electricity is predicted theoretically and validated by finite element (FE) simulation. The complex mechanisms regulating the energy harvesting performance are investigated, focusing particularly on the effects of 3D FG material (FGM) parameters, load resistance, fluid-structure interaction (FSI), and geometry. Numerical results indicate that among several material gradient parameters, the axial gradient index has the most significant impact. Increasing the axial and height gradient indices can markedly enhance the energy harvesting performance. The optimal resistances differ between the first two modes. Overall, the maximum power is generated at lower resistances. The FSI effect can also improve the energy harvesting performance; however, higher flow velocities may destabilize the system, causing failure of harvesting energy. This research is capable of providing new insights into the design of a pipe energy harvester in engineering applications.</p>